A note on a further extension of Gauss’s second summation theorem with an application to the extension of two well-known combinatorial identities

Insuk Kim, Gradimir V. Milovanović*, Richard B. Paris, Arjun K. Rathie

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Recently, Masjed-Jamei and Koepf established the extension of several classical summation theorems (including Gauss’s second summation theorem). Our aim in this paper is to establish a further extension of Gauss’s second summation formulas due to Masjed-Jamei and Koepf in the most general form. The result is then applied to obtain extensions of (i) Knuth’s old sum (or the Reed Dawson identity) and (ii) Riordan’s identity in the most general form. A few interesting results are obtained as special cases of our main findings.

Original language English 10 Quaestiones Mathematicae 12 Jun 2021 https://doi.org/10.2989/16073606.2021.1925368 E-pub ahead of print - 12 Jun 2021

Keywords

• Knuth's old sum
• Reed Dawson identity
• Riordan identity
• Gauss second summation theorem
• Hypergeometric summation formulas and identities